Multi-disciplinary perspective on coupled planet formation and evolution: from accretion to the present-day, from core to crust
Planetary accretion, giant collisions, core formation, magma-ocean crystallization and other important processes during the early days of the solar system set the stage for the long-term evolution of terrestrial planets. These early processes can happen simultaneously or in recurring stages, and are ultimately followed by progressive crustal growth, long-term mantle mixing/differentiation, core-mantle interaction, as well as inner-core crystallization. Indeed, the coupled early and long-term evolution shapes the present-day structure and thermal state of planetary interiors. We seek to gain a better understanding of the formation and evolution of terrestrial bodies by bringing together studies from geophysics, geodynamics, mineral physics, geochemistry, and petrology.
This session welcomes contributions focused on data analysis, modeling and experimental work that address the formation and evolution of terrestrial planets and moons in the Solar System, and around other stars.
Paolo Sossi, Ingo Stotz, Seth Jacobson, Alessandro Morbidelli, and Hugh O'Neill
The Earth is depleted in volatile elements relative to chondritic meteorites, its possible building blocks. Abundances of volatile elements descend roughly log-linearly with their calculated volatilities during solar nebula condensation [1, 2]. This depletion, however, is not accompanied by any stable isotope fractionation, which would otherwise be expected during vaporisation/condensation and atmospheric loss attending accretion [3, 4]. Thus, the physical processes that led to the formation of the Earth are yet to be reconciled with its chemical composition. Here, we integrate N-body simulations of planetary formation  within a framework that combines estimates for the compositions of planetary building blocks with volatile element losses during collisions, to link Earth’s elemental- and isotopic make-up with accretion mechanisms. The smooth pattern of volatile depletion in the Earth reflects the stochastic accretion of numerous, smaller, partially-vaporised precursor bodies whose elemental abundances are set by the heliocentric distances at which they formed. Impact events engender vaporisation, but atmospheric loss is only efficient during the early stages of accretion when volatile species can readily escape the gravitational pull of the proto-Earth. The chemical and isotopic compositions of the most volatile elements are controlled by that of late-accreting material, during which time the proto-Earth is sufficiently large so as to limit atmospheric loss. Stable isotopes of moderately- and highly volatile elements thus retain near-chondritic compositions.
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How to cite:
Sossi, P., Stotz, I., Jacobson, S., Morbidelli, A., and O'Neill, H.: Stochastic accretion of the Earth, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-652, https://doi.org/10.5194/epsc2020-652, 2020.
Estimates of the bulk silicate Moon (BSM) composition have been proposed based on a number of different geochemical, petrological and geophysical arguments but have yet to arrive at a general consensus. In order to obtain further constraints on the BSM composition, we investigated the effect of the BSM FeO content on the physical properties of lunar mantle reservoirs and tested the consistency of different lunar interior models with the bulk Moon density and moment of inertia.
To cover all lunar interior models that are consistent with a given BSM composition, we modeled the properties of the chemical reservoirs forming from lunar magma ocean (LMO) solidification, considered the re-distribution of these reservoirs in the lunar mantle by solid state convection, and calculated the bulk Moon density and moment of inertia of the resulting interior models, assuming varying core properties and selenotherms. Lunar Magma Ocean Crystallization: We modeled LMO cumulate mineralogies using a combination  of crystallization algorithms from the software packages alphaMELTS  and SPICES , that has been validated against recent experiments on LMO fractional crystallization [4, 5]. Thereby we assumed pure fractional crystallization of a deep LMO, that extends to the core-mantle boundary so that the LMO comprises the whole BSM. The bulk LMO composition was chosen based on the estimate of . FeO/MgO ratios of the bulk LMO composition were varied (8.0-13 wt% FeO) to investigate the effect of the FeO content on the densities and mineralogies of individual cumulate layers. All crystals forming in the LMO were assumed to sink and equilibrate with the liquid at the bottom of the magma ocean prior to fractionation, except for plagioclase which was assumed to float to the surface to form anorthositic crust. The average lunar crust thickness was assumed to be 40 km in accordance with recent GRAIL data . Any excess plagioclase that formed after that final crust thickness was reached was assumed to remain in the mantle due to imperfect plagioclase floatation. Mantle Mixing and Overturn: As a consequence of the higher compatibility of lighter Mg compared to denser Fe in the LMO cumulate minerals, the density of the cumulate increases with progressing LMO solidification. Since the LMO solidifies from bottom to top, this results in a gravitationally unstable cumulate stratification that facilitates convective overturn, during which dense material sinks towards the core mantle boundary while lighter material migrates toward the surface. The respective changes in pressure and temperature experienced by individual cumulate layers, as well as mixing and chemical equilibration of different layers during overturn, can affect the mineralogy and physical properties of the lunar mantle. To investigate these effects, we calculated equilibrium mineral parageneses of different cumulate layers using Perple_X . For simplicity we considered five homogeneous cumulate reservoirs (olivine-dominated, pyroxene-dominated, IBC, KREEP and crust), whose compositions were derived from the results of the LMO crystallization models by averaging the compositions of adjacent cumulate layers with similar mineralogies. The mineralogies and densities of each reservoir were calculated as a function of depth along different selenotherms (e.g. ). To evaluate the effect of mixing and chemical equilibration, we also made the same calculations for different compositional mixtures of the layers. The results of these calculations were used as input in a simple density structure model in order to investigate the effect of mantle overturn on the bulk lunar density and moment of inertia. Lunar core sizes and densities were thereby varied within the range of proposed values (e.g. ).
Changing the FeO/MgO ratio of the BSM composition leads to an earlier appearance and higher abundance of Fe-rich minerals in the LMO cumulate. This results in an increased thickness of the late formed, dense ilmenite bearing cumulate (IBC) reservoir, that we defined based on its high density compared to underlying cumulate layers. As a consequence, IBC thickness correlates linearly with the assumed LMO FeO content, varying by a factor of about 4 over the assumed range of FeO contents. Due to its high density the radial distribution of IBC material in the lunar interior has a significant effect on the BSM moment of inertia, even though its volume is comparatively small. The effect of the distribution of IBC on the BSM moment of inertia increases systematically with increasing IBC volume, which is in turn linked to the FeO content. Depending on the chosen core models and selenotherms, realistic bulk Moon densities and BSM moments of inertia could be reached assuming FeO contents of 8-13.5 wt%.
The range of possible FeO contents determined here is valid for a large variation of lunar interior properties and can be narrowed considerably by imposing constraints on the selenotherm, core properties or mantle structure. Seismic and selenodetic data indicate a mantle stratigraphy with a pyroxenitic upper mantle and a dunitic lower mantle  and suggest the presence of a dense, partially molten zone at the core mantle boundary , that might consist of sunken IBC material. These constraints on the interior structure of the lunar mantle indicate that BSM FeO contents of 9 – 11 wt% are most probable. This estimate could be further limited by tighter constraints on the size and density of the lunar core, e.g. by future seismic investigations.
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How to cite:
Schwinger, S. and Breuer, D.: Relationships between Bulk Silicate Moon FeO Content and Bulk Moon Physical Properties, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-739, https://doi.org/10.5194/epsc2020-739, 2020.
Erik Asphaug, Alexandre Emsenhuber, Saverio Cambioni, Travis S. J. Gabriel, and Stephen R. Schwartz
Overview. Terrestrial planets grew in a complex series of late stage giant impacts, and Moon-formation was among last to occur around Earth. But was it a singular event? Here we propose it was three or more episodes involving two bodies and the Sun, an almost-merger followed by an interlude, followed by a merger.
The standard model originated in the 1970s and has been surprisingly resilient . It succeeds at making a Moon-size moon with Moon-like rocky and volatile-depleted composition, and sets the stage for the lunar magma ocean and tidal evolution. The model is only relevant to vimp no faster than ~1.1 vesc, which represents the median velocity of late-stage collisions [3,4]. Larger-velocity collisions encompass the other half of the probability distribution. At one end of the energetic spectrum, Theia could have originated from further out, as proposed by , but these collisions are dynamically disfavored .
To study giant impacts outside the limited realm of efficient mergers, our group has applied machine learning  and physical scaling  to hundreds of high resolution simulations over the expected velocities and impact angles and mass ratios. A definitive conclusion is that hit-and-run collisions (HRCs) are much more probable than mergers in the common velocity range vimp ~1.1−1.4 vesc. They spin up the target, strip mantle from the projectile , and send it back into space along with its remnants − but do not create the Moon (although see ).
The solution we propose (Figure 1) is that Theia is the "runner" from a prior HRC with protoearth. The one-two blow leads to greater mixing and slows the bodies down by tens of percent so they will merge eventually.  found that many or even most late stage accretions are collision chains of varying complexity; on this basis we explore a three-act origin of the Moon: an HRC between prototheia and protoearth; a ~103 to 106 yr interlude featuring sweep-ups and close encounters; and a low-velocity merger resembling the standard model.
The standard model is appealing for astrophysical and petrological reasons. It invokes what seems to be a typical "late stage" accretion of two terrestrial embryos, resulting in an Earth-Moon system of the right mass and angular momentum. And it predicts a volatile-depleted silicate Moon with a small iron core. Also, it is a near-perfect merger of the type that is implicitly assumed in N-body simulations. Under those assumptions runners cannot exist.
To address the major deficiencies of the standard model while preserving its major strengths, we have developed a theoretical basis for a collision chain origin of the Moon. We show it to be a common pathway of planet formation, slowing the random velocities until merger is probable. There are innumerable pathways so it is premature to hone in on one scenario. A scenario meriting further research is an ~0.2 MEarth planet that become a mantle-stripped Theia, that then returns thousands to millions of years later for a merger on a strongly unaligned impact axis.
Modeling.Act I assumes a non-rotating protoearth 0.9 MEarth in circular orbit at 1 AU, of 30/70wt% iron/rock composition. Prototheia is 0.15 MEarth with the same composition and entropy profile. We model representative HRCs with vimp = 1.1 or 1.2 vesc and impact angles θimp = 43° to 55°. These are selected so the runner ends up ~0.1 MEarth to match the standard model. The target neither gains nor loses much mass, but it acquires a rotation period of 8 to 11 hours for these HRCs. No significant disk is produced.
We calculate the egress velocity of the runner, which we then transfer into an N-body code  for Act II. To represent all possible collisions, we clone each SPH outcome into 1000 random orientations and evolve each clone, including the other major planets, until they have another collision with a planet, or for 50 Myr when most giant impact chains are finished. One set of outcomes is shown in Figure 2, where the HRC velocity vimp/vesc = 1.20 (red dashed line) gets slowed down to an egress velocity of 1.01 vesc (black dashed line). Most clones return, tallied in Figure 2 by return velocity and interlude duration. Most return in ~105 years at close to the egress velocity.
By design, Act III resembles the standard model, but with an extra stage of mixing that helps solve the lunar isotope problem and slows the bodies down so that merger is probable. We apply the same compositional and entropy profiles to the target, but give it more mass (0.95 MEarth) and induce a rotation period of 8-12 hours per Act I. Theia, the runner, is now 0.1 MEarth. Some of its mantle comes from protoearth, which would further reconcile the isotopic similarities. Altough every HRC is different, for simplicity we assume one 30/70wt% runner. We set the return velocity as either 1.00 or 1.05 vesc and assume a nominal impact angle of 45°. Another variable is the offset angle between the two collisions, ranging from prograde (0°) to retrograde (180°), which would follow a random distribution . The modeled return collisions are therefore variants of the standard model, and end up with a lunar mass or more in orbit in our simulations.
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How to cite:
Asphaug, E., Emsenhuber, A., Cambioni, S., Gabriel, T. S. J., and Schwartz, S. R.: Moon Formation in Three Acts, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-485, https://doi.org/10.5194/epsc2020-485, 2020.
Teresa Steinke, Duncan van Sliedregt, Kenny Vilella, Wouter van der Wal, and Bert Vermeersen
Intensive tidal heating makes the Galilean satellite Io to an outstanding example of a volcanically active world. Most of the heat generated in the interior is lost through a large number of active volcanoes. The distribution of Io's volcanoes on the surface could help us to constrain properties below Io’s crust, regulating the heat transport mechanism. For this study, we assume that (1) the presence of global volcanism is linked to the presence of melt in the upper mantle; that (2) the large-scale variation in volcanic density is inherited from non-uniform tidal heating and smoothed by vigorous convection; and that (3) the total number of hot-spots is controlled by the spatial frequency of thermal instabilities in the convecting layer. Three unknown parameters are explored: the fraction of convective heat transport compared to magmatic heat transport, the mantle viscosity, and the thickness of the heated layer. In order to evaluate which combinations of interior properties can explain Io's present volcanic distribution, we develop a model based on parameterised heat flow scalings to approximate different spatial characteristics of Io's interior convection pattern. Our model combines internal heating, and convective and magmatic heat flow. Parts of the parameter space that are not in agreement with the observation-derived conditions are ruled out.
Our results show that the observed small- and large-scale characteristics of Io's volcanic pattern can be explained by sub-lithospheric anomalies caused by convection. Solutions that allow for active volcanism and Io's specific large-scale variations in volcanic activity range from a thick mantle of high viscosity (1017 Pa s) to a thin asthenosphere of low viscosity (1012 Pa s). If Io's volcanos are correlated to the spatial frequency of thermal instabilities, the range of Io's total volcanic features between 250 and 3030 can further constrain the parameter space. This favours a mantle with a low melt fraction, a low mantle viscosity, and a magmatic heat transport of >80%.
How to cite:
Steinke, T., van Sliedregt, D., Vilella, K., van der Wal, W., and Vermeersen, B.: Constraints on Io’s interior by combining small- and large-scale characteristics of the volcanic pattern, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-859, https://doi.org/10.5194/epsc2020-859, 2020.
The volatility of an element is defined by its 50% condensation temperature (Tc50) from a canonical nebular gas of Solar composition at 10-4 bar [1, 2]. However, the variability in metallicity and metal/oxygen ratios of extrasolar systems inferred from the spectroscopic measurements of their parent stars [3, 4] implies that the identity, abundance and sequence of condensation may deviate from that of our solar system. As such, planets formed at similar heliocentric distances may be expected to have distinct compositions from those of the terrestrial planets in our solar system. Here we investigate the degree to which nebular composition influences the condensation process by taking nine sets of stellar compositions with variable metallicities that span the range from -0.4 to +0.4 dex and performing Gibbs free energy minimisation calculations with FactSage, including treatment of mineral solid-solutions, over the temperature range 1723 K to 473 K. We find that, although the general order of condensation is similar, absolute values of Tc50 are shifted to higher temperatures at higher dex, where Tc50(S), in particular, increases relative to those of other elements. Condensing nebulae with high metallicities (and also high metal/oxygen ratios) also exhibit the following features: (i) the appearance of reduced assemblages (e.g. CaS oldhamite, forsterite-rich olivine and graphite) in the condensates, (ii) increased fractions of oxygen (relative to its total abundance) locked in the silicate condensates, and (iii) lower fO2 in the gas phase. As a result, these characteristics will lead to significant differences in the chemistry of planetary building blocks, which are then accreted to form telluric planetary bodies.
 Lodders 2003. ApJ 591:1220-1247.
 Wood, B. J., Smythe, D. J., & Harrison, T. 2019. Ame. Miner. 104:844-856.
 Buder, S., Asplund, M., Duong, L. et al. 2018. MNRAS 478:4513:4552.
 Delgado Mena, E., Moya, A., Adibekyan, V., et al. 2019. A&A 624:A78.
How to cite:
Wang, H., Sossi, P., and Quanz, S.: Nebular condensation of different stellar compositions and its influence on planetary chemistry, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-874, https://doi.org/10.5194/epsc2020-874, 2020.
Saverio Cambioni, Seth A. Jacobson, Alexandre Emsenhuber, Erik Asphaug, David C. Rubie, Travis S.J. Gabriel, Roberto Furfaro, and Stephen R. Schwartz
Summary: Inefficient accretion is a common outcome of planet-planet collisions which dominate the late stage of terrestrial planet formation . These giants impacts create deep magma oceans on the resulting bodies , thus promoting multi-step core formation . Here we present how planetary differentiation is affected by inefficient accretion and compare the results to those obtained assuming that collisions are perfectly accretionary (“perfect merging”). We find that the two models provide similar predictions for the mass and core mass fraction of planets more massive than 0.1 Earth’s masses (~1 Mars’ mass), in agreement with previous studies . At smaller scales, however, the inefficient accretion model predicts a higher degree of planetary diversity in terms of core mass fraction. Smaller final planets, by definition, do not participate in many merging giant impacts but may participate in multiple hit and run collisions as either the target or the runner, both of which may leave a strong signal in a small planet's composition. Alternatively, due to the more extensive growth history of larger final planets, these regress to an average composition through the incorporation of many smaller embryos, effectively erasing gross signatures of hit and run collisions.
Why we need to model inefficient accretion: Planet formation models typically assume that, when a target of mass MT accrete a projectile of mass MP, the resulting planet has mass MT + MP (e.g., ). However, numerous studies show that the projectile often manages to escape accretion (hit-and-run collisions, ) and substantial debris can be produced (e.g., [7, 8, 9]). We capture this effect using machine learning [10, 11]. We train neural networks to predict the outcome of the collision (mass of the resulting bodies, their post-impact orbits and core-mass-fractions) from knowledge of the impact properties (target’s and projectile’s masses, and impact angle and velocity). The training, validation and testing set is a large but sparse collection of high-resolution Smoothed Particle Hydrodynamics simulations of giant impacts. We combine the neural networks with rigorous planetary differentiation models ([12, 4]) to study how the chemical equilibrium between the Si- and Fe-rich liquids (the planets’ mantle and the core, respectively) evolve as the pressure, temperature and oxygen fugacity of metal silicate equilibration change because of a giant impact. We assume that every collision is energetic enough to re-equilibrate the planets’ reservoirs. Future work will aim to relax this assumption.
Inefficient accretion versus perfect merging: We first present a case study of a single collision solved using the inefficient accretion model trained on impact simulation data (Figure 1). Where the perfect accretion model would feature a single regime, i.e., the two bodies are assumed to merge in all scenarios, impact simulation results exhibit a richer range of potential outcomes as a function of expected pre-impact conditions. As terrestrial planets conclude their formation in a series of giant impacts , we also study the cumulative effect of such collision chains on the final planets' core mass fraction (Figure 2) using some of the results of the N-body planet formation studies in . These simulations start with the same initial conditions, but in half of them collisions are resolved as perfect merging, while in the other half collisions are modelled using the neural networks. We find that the final planets’ core mass fractions predicted by the inefficient accretion model (dots) agree with those of the perfect merging model (diamonds) for planets’ masses larger than 0.1 Earth masses. This is consistent with previous studies that successfully reproduced Earth’s Bulk Silicate abundances using the results from N-body with perfect merging . At smaller scale, however, the diversity in core mass fraction is enhanced in case inefficient accretion is included. The “degree” of diversity is higher for planets that survived a higher number of hit-and-run collisions, thus linking the collision history of planets to their core mass fractions.
Take home message: Our findings confirm that giant impacts are powerful drivers of planetary diversity, especially for planets less than a few tenths the mass of the largest, e.g. Mars-mass planets in our solar system. A realistic treatment of planetary collisions in terrestrial planet formation is necessary to accurately track compositional evolution.
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How to cite:
Cambioni, S., Jacobson, S. A., Emsenhuber, A., Asphaug, E., Rubie, D. C., Gabriel, T. S. J., Furfaro, R., and Schwartz, S. R.: The Effect of Inefficient Accretion on Planetary Differentiation, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-407, https://doi.org/10.5194/epsc2020-407, 2020.
Observations of Earth-sized exoplanets are mostly limited to information on their masses and radii. Simple mass-radius relationships have been developed for scaled-up versions of Earth or other planetary bodies such as Mercury and Ganymede, as well as for one-material spheres made of pure water(-ice), silicates, or iron. However, they do not allow a thorough investigation of composition influences and thermal state on a planet’s interior structure and properties.
As shown in Figure 1, we investigate the structure of a rocky planet shortly after formation and at later stages of thermal evolution assuming the planet is differentiated into a metal core and a rocky mantle (consisting of Earth-like minerals, but with a variable iron content).
Fig. 1: Temperature (left), pressure (centre), and density (right) profiles for two example planet masses of one and two Earth masses considering the hot temperature scenario and assuming di erent planet iron contents. From Noack and Lasbleis, 2020.
We derived possible initial temperature profiles after the accretion and magma ocean solidification following Stixrude (2014). We then developed parameterisations for the thermodynamic properties inside the core depending on planet mass, composition, and thermal state. We provide the community with robust scaling laws for the interior structure, temperature profiles, and core- and mantle-averaged thermodynamic properties for planets composed of Earth’s main minerals but with variable compositions of iron and silicates, see Figure 2.
Fig. 2: Comparison between interior structure model data (filled circles) and predicted data from our parameterised model (black empty circles) for different planet parameters and planet masses, with colours ranging from 0.8 (dark blue) to 2 (yellow) Earth masses. Grey circles show the individual errors. The mean error with one standard deviation is listed for each error plot. From Noack and Lasbleis, 2020.
The interior structure profiles, an online tool and the link to the repository including all Python Jupyter notebooks, that were needed to derive the scaling laws and figures of this study, as well as an implementation of the scaling laws in Python are available on the following website: http://geodyn-chic.de/tools.
The scaling laws make it possible to investigate variations in thermodynamic properties for different interior thermal states in a multitude of applications such as deriving mass-radius scaling laws or estimating magnetic field evolution and core crystallisation for rocky exoplanets.
Stixrude, L. 2014, Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci., 372, 20130076
Noack, L. and Lasbleis, M. 2020, A&A, 638, A129
How to cite:
Noack, L. and Lasbleis, M.: Parameterisations of interior properties of rocky planets, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-947, https://doi.org/10.5194/epsc2020-947, 2020.
Alix Seegers, Kirsten van Zuilen, Riemer Stelwagen, Wim van Westrenen, and Pieter Vroon
Present geochemical models of planetary core formation commonly focus on either element abundances or isotope fractionation between mantle and core. Data gathered from these two techniques can be mutually inconsistent, leading to different conclusions concerning core formation processes. An example of this is the Si content of the Earth’s core. Element partitioning data and seismological observations indicate that the Earth’s core only contains minor amounts of Si , whereas isotopic data suggests significant amounts of Si may be present .
To address this data discrepancy problem, this study combines element partitioning behaviour and isotope fractionation of Fe and Zn through metal-silicate partitioning experiments. Metal-silicate partitioning experiments at high pressure and temperature allow for the distribution of elements and their isotopes between planetary cores (metal) and mantles (silicate) to be studied under controlled conditions [e.g. 6,7, 10]. As during planetary core formation it is assumed that some form of equilibrium is reached over millions of years, the experiments should reflect this as well. Therefore, it is essential to determine the time that is required for every experiment to achieve both elemental and isotopic abundance equilibrium.
Metal-silicate partitioning experiments are performed under high pressure and temperature conditions using an end-loaded piston-cylinder press. To solely focus on the equilibration times, experiments of the same starting compositions were subjected to peak conditions of 1GPa and 1823K for a time ranging from 3 minutes up to 12 hours. The experiments consisted of a synthetic analogue of the lunar Apollo 15 Green Glass as silicate phase , along with a metal phase of Fe-metal doped with Zn.
Element concentrations of metal and silicate phases of every experiment were measured with an electron microprobe (EMPA) for major elements and laser ablation ICP-MS (LA-ICP-MS) for trace elements. To analyse Fe and Zn isotopic fractionation, both Zn and Fe were isolated from the metal- and silicate phases through ion-exchange chromatography. The AG-X8 resin was used for the separation of Fe, and the AG-MP-1 resin for Zn . The isotopes of Fe and Zn were subsequently measured using a multi-collector ICP-MS (MC-ICP-MS) with a double spike technique. The precision of the isotope analyses is determined by measuring isotopic reference materials. The standards IRMM-014 (Fe) and ETH-ZN indicate a precision of ± 0.03‰ (2SD) for Fe isotopes and ± 0.05‰ (2SD) for Zn isotopes respectively. Additionally, rock standards such as BHVO-2, BCR-2, AGV-2 and BIR-1 that had been processed exactly like the experiments were measured during the analyses.
Experimental run products typically show a good separation of a metallic phase and quenched silicate melt. Disequilibrium within experiments can cause heterogeneous spots where groups of elements are clustered. These heterogeneous spots can be seen in experiments of run times of e.g. 3 and 5 minutes (Fig. 1), whereas they are absent in experiments with longer run times (Fig. 2). Results shown in Fig. 3 confirm these observations as the measured elements from short (<10 minutes) experiments show different partitioning behaviour compared to longer experiments (>30 minutes). Therefore, concentration analyses indicate that elemental equilibrium is reached within 30 minutes.
Isotope equilibration times are significantly longer than concentration equilibration times (Fig. 4 and 5) . Within the first two hours of an experiment, the fractionation factors Δ56Femetal-silicate and Δ66Znmetal-silicate are positive and variable. Between 2-4 hours, the fractionation factors become negative and start to stabilise. After approximately 4 hours, isotopic equilibrium is reached for both Fe and Zn with Δ56Femetal-silicate = -0.04‰ ± 0.07 and Δ66Znmetal-silicate = -0.11‰ ± 0.06, which corresponds with literature data [2,4].